Using genetic algorithms to estimate local shape parameters of RBFs

Abstract

Estimation of design rainfall in unobservable places is important in hydrological engineering. The aim of this paper is to use genetic algorithms to find the optimal global and local shape parameters of radial basis functions (RBFs) to create an interpolation model to estimate scaling exponents of short term rainfalls across selected regions of Slovakia. Scaling exponents can be used later to estimate rainfalls intensity in places without observations. In this paper, we have used interpolation methods based on RBFs to model interpolation surfaces. We investigate the properties of shape parameters in RBFs, and we test some methods for finding an optimal shape parameter. The choice of the best basis function along with the optimal shape parameter has a significant impact on the accuracy of the interpolation models which best approximate the real model. We have found that Hardy’s multiquadrics interpolant with the optimal local shape parameters can be used for estimation the rainfall intensities in areas without direct observation.